UNIVERSITY OF SCIENCE FINAL EXAM Subject: Statistics for Ecology Topic: Analysis of presence or absence of species Requirement: The data to be analyzed is the data on the abundance of Faramea occidentalis (in attached text file) Please explain the influence of precipitation, altitude, age and geology parameters on the presence-absence of Faramea occidentalis species The calculation and the numerical results are required Full name: Bui Thi Hao Class: K55 of Advanced Program of Environmental Science Student’s code: 1000739 Content: Page A Load the data from external file B Doing analysis I Explanation with single explanatory variable a Explain the influence of Age categories b Explain the influence of elevation(i.e.altitude) c Explain the influence of Precipitation d Explain the influence of Geology II Explanation with several explanatory variables SOLUTION A Load the data from external file B Doing analysis Due to the more comprehensive analysis of frequencies, I prefer to use GLMgeneralized linear model (binomal or quasibinomal flexibly) I Explanation with single explanatory variable a Explain the influence of Age on the presence-absence of species From using Biodiversity.R, I got the result as above The result shows the coefficients of Age.categories (in logit value) However, more important, the deviance residuals and Pr-value should be concerned According to the above results, the variance of presence/absence of Faramea occidentalis depending on age.categories explained only 3.0793 per 59.401 of null deviance (5.18%) (very small) Especially, that Pr-value ~ 0.2508 in the ANOVA table is so high implies there is evidence so that coefficients of categories equal zero It means age categories have no effect on the presence/absence of species In conclusion, the age categories in their own have no contribution on explaining the presence/absence of Faramea occidentalis b Explain the influence of elevation(i.e.altitude) on the presence-absence of species From using Biodiversity.R, I got the result as above The result shows the coefficients of Elevation (in logit value), as well as, the deviance residuals and Pr-value According to the above results, the variance of presence/absence of Faramea occidentalis depending on elevation explained only 9.9317 per 59.401 of null deviance (16.72%) (so small) However, that Pr-value ~ 0.0357 is very low implies there is evidence so that coefficients of elevation not equal zero It means, elevation still has certain effect on the presence/absence of species In conclusion, the elevation in its own has contribution on explaining the presence/absence of Faramea occidentalis (but not clear and strong due to small explained deviance) according to the following link fuction: Logit(µ)= 1.0595-0.00784x = y Where µ: the mean of presence/absence value x: the elevation value (should be the mean value of certain interval)  µ= exp(y)/(1+exp(y)) c Explain the influence of Precipitation on the presence-absence of species The above result shows the coefficients of precipitation (in logit value), as well as, the deviance residuals and Pr-value Accordingingly, the variance of presence/absence of Faramea occidentalis depending on precipitation explained only 8.8406 per 59.401 of null deviance (14.88%) (so small) However, that Pr-value ~ 0.0172 is very low implies there is evidence so that coefficients of precipitation not equal zero It means, precipitation still has certain effect on the presence/absence of species In conclusion, the precipitation in its own has contribution on explaining the presence/absence of Faramea occidentalis ((but not clear and strong due to small explained deviance) according to the following link fuction: Logit(µ)= 6.9483-0.00272x = y Where µ: the mean of presence/absence value  µ= exp(y)/(1+exp(y)) x: the precipitation value ((should be the mean value of certain interval) d Explain the influence of Geology on the presence-absence of species The above result shows the coefficients of geology (in logit value), as well as, the deviance residuals and Pr-value Accordingingly, the variance of presence/absence of Faramea occidentalis depending on geology explained 25.548 per 59.401 of null deviance (43%) (noticeable) Moreover, that Pr-value ~ 0.002027 in the ANOVA table is very low implies there is evidence so that coefficients of geology not equal zero It means, v has certain effect on the presence/absence of species In conclusion, the geology in its own has contribution on explaining the presence/absence of Faramea occidentalis according to the following link fuction: Logit(µ)= intercept + coefficient for geology category = y Where µ: the mean of presence/absence value  µ= exp(y)/(1+exp(y)) Example: For GeologyTc: Logit(µ)= -2.0794+2.367 = 0.2876 => µ= 57.14 % II Explanation with several explanatory variables Is there more complex pattern in relationship of explanory variables on explaining response varible => Use binomal GLM on several explanatory variables As we know, AIC (Akaike Information Criterion) is to provide us information about combination of simplicity and explained deviance A model with a lower AIC has a better combination of simplicity and explained deviance, therefore be more prefered than that with the higher AIC  It is better to use model with ( Precipitation + Precipitation^2 + Age Cat + Geology + Elevation^2) rather than (Precipitation + Precipitation^2 + Age Cat + Geology + Elevation+ Elevation^2), and than (Precipitation+ Age Cat + Geology + Elevation) (since AIC respectively: 42.020 < 43.376 < 43.969) In conclusion, the best model is binomal GLM on Precipitation + Precipitation^2 + Age Cat + Geology + Elevation^2 As above result, this model can explain up to (59.401-18.020)/59.401= 69.66% of null deviance of dataset (much higher than that off all the models with single explanatory variable) Moreover, in the single term deletions, the deletion of any term will cause the increase of AIC, i.e the less combination of simplicity and explained deviance That means all of mentioned terms should be kept in the model, and the link function would be: Y= Logit(µ)= -8.830e + 8.031e^-2.x -1.765e^-5.x2+ y+z-6.407e^-5.k Where: µ: the mean of presence/absence value => µ= exp(Y)/(1+exp(Y)) x: the precipitation value z: coefficient for age category y: coefficient for geology category k: the elevation value 10 Conclusion: Each explanatory variable (precipitation, altitude, age and geology) has its own influence on response variable ( the presence/absence of Faramea occidentalis) at certain level (even zero level-no influence) More obviously, however, the complex pattern in which all explanatory variables are included is much better in explaining the presence/absence of species, so such a model should be more prefered 11